In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following:

  • takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure),
  • returns a function as its result.

All other functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function.

(“Higher-Order Function” 2022)